The specific aim of this exploratory investigation is to introduce a novel approach to enhance ultrasonic image resolution and, in parallel, examine the feasibility of tissue characterization by exploiting the scaling signature of ultrasound-matter interactions in general, and tissue in particular. One of the key objectives of the proposed work is to broaden the bandwidth of the signal obtained via conventional transducers. The work is motivated by a bandwidth broadening technique which was successfully implemented in a recent speech enhancement work in our laboratory. This approach is based on the extraction and modeling of the lower-law of 1/f/alpha noise component of the narrow-band signal which, in turn, allows us to synthesize higher frequency scales. This creates the effect of data collected over wider band of frequencies and is expected to enhance the resolution of ultrasonic medical images by recovering the frequencies of the original transmitted signal lost due to the attenuation mechanisms in the tissue. The modeling stage in the processing scheme exploits the geometric structure of the scale-to-scale variance progression of the wavelet coefficients. A natural dual use for this analysis step is to investigate the validity of this measure as a means for tissue characterization. Moreover, the resulting wide-band data can be used in conjunction with other signaling processing algorithms such as Split Spectrum Processing to further improve image quality for tumor detection.